A001836 Numbers k such that phi(2k-1) < phi(2k), where phi is Euler's totient function A000010. (Formerly M5429 N2359)

53, 83, 158, 263, 293, 368, 578, 683, 743, 788, 878, 893, 908, 998, 1073, 1103, 1208, 1238, 1268, 1403, 1418, 1502, 1523, 1658, 1733, 1838, 1943, 1964, 2048, 2063, 2153, 2228, 2243, 2258, 2363, 2393, 2423, 2468, 2558, 2573, 2633, 2657, 2678

Offset

1,1

References

Jeffrey Shallit, personal communication.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

T. D. Noe, Table of n, a(n) for n = 1..1000

V. L. Klee, Jr., Some remarks on Euler's totient function, Amer. Math. Monthly, 54 (1947), 332.

Don Reble, Python program.

J. Shallit, Letter to N. J. A. Sloane, Jul 17 1975.

Maple

with(numtheory): A001836:=n->`if`(phi(2*n-1) < phi(2*n), n, NULL): seq(A001836(n), n=1..5*10^3); # Wesley Ivan Hurt, Oct 10 2014

Mathematica

Select[Range[3000], EulerPhi[2# - 1] < EulerPhi[2#] &] (* Harvey P. Dale, Apr 01 2012 *)
Position[Partition[EulerPhi[Range[6000]], 2], _?(#[[1]]<#[[2]]&), 1, Heads-> False]//Flatten (* Harvey P. Dale, Jul 02 2021 *)

Prog

(PARI) is(n)=eulerphi(2*n-1)<eulerphi(2*n) \\ Charles R Greathouse IV, Feb 21 2013
(Haskell)
a001836 n = a001836_list !! (n-1)
a001836_list = f a000010_list 1 where
   f (u:v:ws) x = if u < v then x : f ws (x + 1) else f ws (x + 1)
-- Reinhard Zumkeller, Jul 11 2014
(Python)
from sympy import totient
def ok(n): return totient(2*n - 1) < totient(2*n) # Indranil Ghosh, Apr 29 2017

Crossrefs

Cf. A000010, A001837.

Sequence in context: A234102 A234104 A212420 * A144939 A118149 A251144

Adjacent sequences: A001833 A001834 A001835 * A001837 A001838 A001839

Keyword

nonn,nice

Author

N. J. A. Sloane

Extensions

Corrected and extended by Don Reble, Jan 04 2007

Status

approved